Emily Analysis
2026-02-03
| Characteristic | Overall N = 1801 |
ABC N = 301 |
ACB N = 301 |
BAC N = 301 |
BCA N = 301 |
CAB N = 301 |
CBA N = 301 |
p-value2 |
|---|---|---|---|---|---|---|---|---|
| Age (years) | 32 (8) [18, 45] | 33 (8) [19, 44] | 31 (7) [18, 42] | 31 (7) [20, 44] | 33 (8) [19, 45] | 32 (7) [21, 44] | 31 (7) [20, 44] | 0.6 |
| Race | 0.9 | |||||||
| Â Â Â Â Black | 64 (36%) | 12 (40%) | 13 (43%) | 12 (40%) | 10 (33%) | 8 (27%) | 9 (30%) | |
| Â Â Â Â White | 52 (29%) | 8 (27%) | 9 (30%) | 7 (23%) | 7 (23%) | 12 (40%) | 9 (30%) | |
| Â Â Â Â Other | 64 (36%) | 10 (33%) | 8 (27%) | 11 (37%) | 13 (43%) | 10 (33%) | 12 (40%) | |
| Female | 81 (45%) | 13 (43%) | 11 (37%) | 16 (53%) | 14 (47%) | 12 (40%) | 15 (50%) | 0.8 |
| 1 Mean (SD) [Min, Max]; n (%) | ||||||||
| 2 Kruskal-Wallis rank sum test; Pearson’s Chi-squared test | ||||||||
preliminary assessment and comparison of systemic and local Pharmacokinetics (PK) of Pill A, Gel B, and Gel C
No apparent difference in starting value by period or treatment, so looking at change from baseline in PK
Carryover effects and period were excluded for parsimony, as the likelihood ratio test indicated that they did not significantly improve model fit
Notation: \(i =\) subject, \(j =\) treatment,
\[ \begin{align} Y_{ij} &= \mu + b_{i} + \tau_j + \varepsilon_{ij},\\ b_{i} &\sim N(0, \sigma_i^2), \\ \varepsilon_{ij} &\sim N(0, \sigma^2), \end{align} \]
Blood PK Change by Treatment
Findings: Significantly less decrease in gels vs pill A
## Model df AIC BIC logLik Test L.Ratio p-value
## model 1 5 4922.711 4944.169 -2456.356
## model_large 2 8 4927.185 4961.517 -2455.592 1 vs 2 1.526705 0.6761## Linear mixed-effects model fit by maximum likelihood
## Data: merged
## AIC BIC logLik
## 4922.711 4944.169 -2456.356
##
## Random effects:
## Formula: ~1 | ptid
## (Intercept) Residual
## StdDev: 6.448611 22.01428
##
## Fixed effects: bloodVL_change ~ treatment
## Value Std.Error DF t-value p-value
## (Intercept) 121.16111 1.714566 358 70.66576 0
## treatmentGel B -10.88889 2.326981 358 -4.67941 0
## treatmentGel C -11.65556 2.326981 358 -5.00887 0
## Correlation:
## (Intr) trtmGB
## treatmentGel B -0.679
## treatmentGel C -0.679 0.500
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.75160265 -0.61117874 0.02663025 0.63949249 2.39871344
##
## Number of Observations: 540
## Number of Groups: 180
Skin PK Change by Treatment
Findings: Significantly less decrease in gels vs pill A
## Model df AIC BIC logLik Test L.Ratio p-value
## model 1 5 5424.874 5446.332 -2707.437
## model_large 2 8 5430.205 5464.538 -2707.103 1 vs 2 0.6684288 0.8806## Linear mixed-effects model fit by maximum likelihood
## Data: merged
## AIC BIC logLik
## 5424.874 5446.332 -2707.437
##
## Random effects:
## Formula: ~1 | ptid
## (Intercept) Residual
## StdDev: 0.007291377 36.40963
##
## Fixed effects: skinVL_change ~ treatment
## Value Std.Error DF t-value p-value
## (Intercept) 205.52778 2.721384 358 75.52326 0
## treatmentGel B -32.40556 3.848618 358 -8.42005 0
## treatmentGel C -41.92222 3.848618 358 -10.89280 0
## Correlation:
## (Intr) trtmGB
## treatmentGel B -0.707
## treatmentGel C -0.707 0.500
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.43651408 -0.59180005 0.04600431 0.72493020 3.19680343
##
## Number of Observations: 540
## Number of Groups: 180
assess the correlation of PK with adherence measures and the occurrence of adverse events
Carryover effects and period were excluded for parsimony, as the likelihood ratio test indicated that they did not significantly improve model fit
Q: include treatment X adherence and treatment X AE interaction terms???
Skin PK
Skin/Blood PK ~ Random Intercept (Subject) + Treatment + Adherence + Carryover + Period
## Model df AIC BIC logLik Test L.Ratio p-value
## model 1 7 5307.160 5337.201 -2646.580
## model_large2 2 11 5290.549 5337.757 -2634.275 1 vs 2 24.61057 0.0001## Linear mixed-effects model fit by maximum likelihood
## Data: merged
## AIC BIC logLik
## 5307.16 5337.201 -2646.58
##
## Random effects:
## Formula: ~1 | ptid
## (Intercept) Residual
## StdDev: 0.003649564 32.52911
##
## Fixed effects: skinVL_change ~ treatment + overall_adhere + overall_safety
## Value Std.Error DF t-value p-value
## (Intercept) 162.22787 7.582825 356 21.394119 0
## treatmentGel B -24.41464 3.625130 356 -6.734832 0
## treatmentGel C -36.99593 3.543320 356 -10.441036 0
## overall_adhere 1.81506 0.274724 356 6.606870 0
## overall_safety1 -55.77639 5.201704 356 -10.722715 0
## Correlation:
## (Intr) trtmGB trtmGC ovrll_
## treatmentGel B -0.509
## treatmentGel C -0.443 0.534
## overall_adhere -0.945 0.311 0.234
## overall_safety1 0.139 -0.079 -0.032 -0.205
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.43058828 -0.67881147 0.02915247 0.64404884 3.53027310
##
## Number of Observations: 540
## Number of Groups: 180## Linear mixed-effects model fit by maximum likelihood
## Data: merged
## AIC BIC logLik
## 5290.549 5337.757 -2634.275
##
## Random effects:
## Formula: ~1 | ptid
## (Intercept) Residual
## StdDev: 0.004174974 31.79624
##
## Fixed effects: skinVL_change ~ treatment * overall_adhere + treatment * overall_safety
## Value Std.Error DF t-value p-value
## (Intercept) 238.04771 21.667665 352 10.986311 0.0000
## treatmentGel B -108.95724 23.377772 352 -4.660719 0.0000
## treatmentGel C -122.25653 23.950925 352 -5.104460 0.0000
## overall_adhere -1.13762 0.818852 352 -1.389291 0.1656
## overall_safety1 -29.61261 8.743642 352 -3.386759 0.0008
## treatmentGel B:overall_adhere 3.40490 0.904914 352 3.762682 0.0002
## treatmentGel C:overall_adhere 3.39045 0.924719 352 3.666464 0.0003
## treatmentGel B:overall_safety1 -40.84761 12.155471 352 -3.360430 0.0009
## treatmentGel C:overall_safety1 -37.04463 12.856933 352 -2.881296 0.0042
## Correlation:
## (Intr) trtmGB trtmGC ovrll_ ovrl_1 trGB:_ trGC:_
## treatmentGel B -0.927
## treatmentGel C -0.905 0.838
## overall_adhere -0.993 0.921 0.899
## overall_safety1 0.114 -0.106 -0.103 -0.148
## treatmentGel B:overall_adhere 0.899 -0.986 -0.813 -0.905 0.134
## treatmentGel C:overall_adhere 0.880 -0.815 -0.988 -0.886 0.131 0.801
## treatmentGel B:overall_safety1 -0.082 0.117 0.074 0.107 -0.719 -0.171 -0.094
## treatmentGel C:overall_safety1 -0.078 0.072 0.111 0.101 -0.680 -0.091 -0.158
## tGB:_1
## treatmentGel B
## treatmentGel C
## overall_adhere
## overall_safety1
## treatmentGel B:overall_adhere
## treatmentGel C:overall_adhere
## treatmentGel B:overall_safety1
## treatmentGel C:overall_safety1 0.489
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.405995796 -0.615618058 0.002664942 0.610769689 3.605667548
##
## Number of Observations: 540
## Number of Groups: 180
Blood PK
## Model df AIC BIC logLik Test L.Ratio p-value
## model 1 7 4860.258 4890.299 -2423.129
## model_large2 2 11 4851.039 4898.246 -2414.519 1 vs 2 17.21954 0.0018## Linear mixed-effects model fit by maximum likelihood
## Data: merged
## AIC BIC logLik
## 4860.258 4890.299 -2423.129
##
## Random effects:
## Formula: ~1 | ptid
## (Intercept) Residual
## StdDev: 4.74164 21.00209
##
## Fixed effects: bloodVL_change ~ treatment + overall_adhere + overall_safety
## Value Std.Error DF t-value p-value
## (Intercept) 98.73209 5.172962 356 19.086184 0.0000
## treatmentGel B -6.81051 2.354117 356 -2.893020 0.0041
## treatmentGel C -9.10003 2.295483 356 -3.964320 0.0001
## overall_adhere 0.93216 0.187884 356 4.961396 0.0000
## overall_safety1 -26.34806 3.460017 356 -7.615009 0.0000
## Correlation:
## (Intr) trtmGB trtmGC ovrll_
## treatmentGel B -0.513
## treatmentGel C -0.443 0.538
## overall_adhere -0.949 0.327 0.247
## overall_safety1 0.131 -0.079 -0.032 -0.195
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.5553528690 -0.5673073777 0.0005900677 0.6043037231 3.0550971969
##
## Number of Observations: 540
## Number of Groups: 180## Linear mixed-effects model fit by maximum likelihood
## Data: merged
## AIC BIC logLik
## 4851.039 4898.246 -2414.519
##
## Random effects:
## Formula: ~1 | ptid
## (Intercept) Residual
## StdDev: 5.176441 20.56066
##
## Fixed effects: bloodVL_change ~ treatment * overall_adhere + treatment * overall_safety
## Value Std.Error DF t-value p-value
## (Intercept) 131.74236 14.431943 352 9.128525 0.0000
## treatmentGel B -39.19101 15.315595 352 -2.558895 0.0109
## treatmentGel C -52.11513 15.650359 352 -3.329964 0.0010
## overall_adhere -0.36462 0.545375 352 -0.668563 0.5042
## overall_safety1 -11.39117 5.811353 352 -1.960158 0.0508
## treatmentGel B:overall_adhere 1.31391 0.591905 352 2.219795 0.0271
## treatmentGel C:overall_adhere 1.73440 0.603583 352 2.873511 0.0043
## treatmentGel B:overall_safety1 -25.67859 8.049524 352 -3.190076 0.0016
## treatmentGel C:overall_safety1 -17.98165 8.518057 352 -2.111003 0.0355
## Correlation:
## (Intr) trtmGB trtmGC ovrll_ ovrl_1 trGB:_ trGC:_
## treatmentGel B -0.924
## treatmentGel C -0.901 0.841
## overall_adhere -0.993 0.919 0.895
## overall_safety1 0.113 -0.109 -0.107 -0.147
## treatmentGel B:overall_adhere 0.895 -0.986 -0.816 -0.901 0.138
## treatmentGel C:overall_adhere 0.875 -0.818 -0.988 -0.881 0.135 0.804
## treatmentGel B:overall_safety1 -0.080 0.118 0.075 0.104 -0.717 -0.173 -0.096
## treatmentGel C:overall_safety1 -0.075 0.073 0.113 0.098 -0.678 -0.093 -0.160
## tGB:_1
## treatmentGel B
## treatmentGel C
## overall_adhere
## overall_safety1
## treatmentGel B:overall_adhere
## treatmentGel C:overall_adhere
## treatmentGel B:overall_safety1
## treatmentGel C:overall_safety1 0.492
##
## Standardized Within-Group Residuals:
## Min Q1 Med Q3 Max
## -3.63070078 -0.59111860 -0.02603496 0.59219448 2.76927257
##
## Number of Observations: 540
## Number of Groups: 180